Quasisymmetric graphs and Zygmund functions

Leonid V. Kovalev; Jani Onninen

doi:10.1007/s11854-012-0039-x

Quasisymmetric graphs and Zygmund functions

Leonid V. Kovalev, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class Λ*. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps. Kovalev was supported by the NSF grant DMS-0968756.

Original language	English (US)
Pages (from-to)	343-361
Number of pages	19
Journal	Journal d'Analyse Mathematique
Volume	118
Issue number	1
DOIs	https://doi.org/10.1007/s11854-012-0039-x
State	Published - Oct 2012

ASJC Scopus subject areas

Analysis
General Mathematics

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10.1007/s11854-012-0039-x

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author = "Kovalev, {Leonid V.} and Jani Onninen",

note = "Funding Information: ∗Kovalev was supported by the NSF grant DMS-0968756. †Onninen was supported by the NSF grant DMS-1001620.",

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Quasisymmetric graphs and Zygmund functions

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